Hi;
I am having difficulty using the Disk[] primitive to define my integration region - see attached. This method is quite new to me, however it seems really elegant, and I would sure like to learn how to use it correctly.
Thanks,Mitch Sandlin
You can try IntegrateChangeVariables:
IntegrateChangeVariables
IntegrateChangeVariables[ Inactive[Integrate][Cos[Sqrt[x^2 + y^2]], Element[{x, y}, Disk[]]], {r, \[Theta]}, "Cartesian" -> "Polar"]
I'm not sure how mathematically rigorous this is, but it seems to me that if you want to change the coordinate system, then you need to change the region:
Integrate[Cos[r] r, {r, t} \[Element] Rectangle[{0, 0}, {1, 2 Pi}]]
All the examples I can find for using region-like primitives as integration regions use Cartesian coordinates rather than polar. So your integral would be written
In[95]:= Integrate[Cos[Sqrt[x^2 + y^2]] , {x, y} \[Element] Disk[{0, 0}, 1]] Out[95]= 2 \[Pi] (-1 + Cos[1] + Sin[1])
